The following site (http://www-ist.massey.ac.nz/dstirlin/CAST/CAST/Hcausal/causal_c2.html) defines a causal relationship as one where one variable 'directly' affects the other, but without the other variable having any influence on the first variable. However, the following site (http://medical-dictionary.thefreedictionary.com/direct+causal+association) defines a direct causal relationship as one where one variable causes a change in the other and there are no intervening variables.
However, both definitions are different. You can have a relationship with no intervening variables, but one where both variables directly affect each other. One wouldn't dare call this a correlation, but according to the first definition that wouldn't be a causation either.
Moreover, I assume that there are relationships where there are intervening variables but where one variable can cause a change in the other without the reverse being possible. According to the second definition, this wouldn't be a causation.
This begs the question: is there a difference between a causal relationship and a DIRECT causal relationship?
Best Answer
Causal relationships can be direct or indirect. That is, direct causal relationships are a special case of causal relationships. For example, in $A \rightarrow B \rightarrow C$, the node $A$ is a cause of $C$ but it affects $C$ through $B$, so although there is a causal relationship between $A$ and $C$, this is an indirect causal relationship.
About the relationship between causation and correlation, note that "correlation does not imply causation". For example, in $B \leftarrow A \rightarrow C$, $B$ and $C$ are correlated but do not have any causal relationship.